Quantized invariant tori in Andreev billiards of mixed phase Space.

Kaufman, Z. and Kormanyos, A. and Cserti, J. and Lambert, Colin J. (2006) Quantized invariant tori in Andreev billiards of mixed phase Space. Physical review B, 73 (21). p. 214526. ISSN 1098-0121

Abstract

Comparing the results of exact quantum calculations and those obtained from the Einstein-Brillouin-Keller–like quantization scheme of Silvestrov et al. [Phys. Rev. Lett. 90, 116801 (2003)] we show that the spectrum of Andreev billiards of mixed phase space can basically be decomposed into a regular and an irregular part, similarly to normal billiards. We provide a numerical confirmation of the validity of this quantization scheme for individual eigenstates and discuss its accuracy.